The present book consists of an introduction and six
chapters. The introduction discusses basic notions and definitions of
the traditional course of mathematical physics and also mathematical
models of some phenomena in physics and engineering. Chapters 1 and 2
are devoted to elliptic partial differential equations. Here much
emphasis is placed on the Cauchy- Riemann system of partial differential
equations, that is on fundamentals of the theory of analytic functions,
which facilitates the understanding of the role played in mathematical
physics by the theory of functions of a complex variable.
Chapters 3 and 4 the structural properties of the solutions of
hyperbolic and parabolic partial differential equations are studied and
much attention is paid to basic problems of the theory of wave equation
and heat conduction equation.
In Chapter 5 some elements of the
theory of linear integral equations are given. A separate section of
this chapter is devoted to singular integral equations which are
frequently used in applications. Chapter 6 is devoted to basic practical
methods for the solution of partial differential equations. This
chapter contains a number of typical examples demonstrating the essence
of the Fourier method of separation of variables, the method of integral
transformations, the finite difference method, the melthod of
asymptotic expansions and also the variational methods.
the book it is sufficient for the reader to be familiar with an ordinary
classical course on mathematical analysis studied in colleges. Since
such a course usually does not involve functional analysis, the
embedding theorems for function' spaces are not included in the present
The book was translated from the Russian by V. M. Volosov and I. G. Volosova and was first published by Mir Publishers in 1980.